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Research on Cost-benefit Evaluation Model for Performance-based fire Safety Design of Buildings
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 135 (2016) 536 – 542
Research on cost-benefit evaluation model for performance-based fire safety design of buildings You-wei Zhang* Chinese People’s Armed Police Force Academy, 220 Xichang Road, Langfang 065000, China
Abstract One of the most important functions of performance-based fire safety design method is to evaluate the economic efficiency of different schemes so that to make the fire safety investment more reasonable. It should begin with the calculation of cost budgets and benefits when evaluate the investment efficiency. Costs for improving building fire resistance and installing fire engineering projects are included in the investment budgets. However, the investment benefits are mainly about the reduced losses after the enhancement of the building fire safety level. Based on the performance-based fire safety design method, applying principles of economics and construction budget, the model described above will be built in this paper to provide scientific guides for fire safety investment. © Authors. Published by Elsevier Ltd. This an open accessunder articleCC under the CC BY-NC-ND ©2016 2016The The Authors. Published by Elsevier Ltd.isOpen access BY-NC-ND license. license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of School of Engineering of Sun Yat-sen University. Peer-review under responsibility of the organizing committee of ICPFFPE 2015
.
Keywords: performance-based fire safety design; cost-benefit analysis; cost budget; loss estimation
Nomenclature
cost of doors
cidoor c jwin
cost of window j
CWIN
cost of windows
ckwall
cost of wall k
CWALL
cost of walls
clother
cost of other component l
COther n
cost of columns, beams, floors and roofs
CEG
cost of fire protection engineering projects
amount of doors
CINSTALL
cost of fire protection installation projects
m
amount of windows
cost of fire protection maintaining projects
p q yC DL IL
amount of walls amount of others probability of damage direct loss of building in a fire indirect loss of building in a fire
CMAINTAIN F A xC L AT
AS
areas damaged by smoke (m2)
AW
areas damaged by water (m2)
PTD
probability of temperature damage
PSD
probability of smoke damage
CBC
cost of building structure
CDOOR
cost of door i
an investment in a year future an investment in each year future maximum value of factor causing damage total losses of building in a fire areas damaged by temperature (m2)
* Corresponding author. Tel.: +86-13503260747. E-mail address: [email protected]
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICPFFPE 2015
doi:10.1016/j.proeng.2016.01.096
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Aoverlap
PWD
probability of temperature damage
G
an increasing amount of investment in each year future (Yuan)
areas damaged by three factors(m2)
Poverlap probability of damage caused by three factors
ZW
density of possessions’ value caused by water (Yuan/m2)
ZT
density of possessions’ value caused by temperature (Yuan/m2)
ZS
density of possessions’ value caused by smoke (Yuan/m2)
P
present worth of each investment in the future areas enclosed by FDS temperature curve and time axis
AFDS
ASTANDARD areas enclosed by standard fire temperature curve and time axis 1. Introduction Performance-based fire safety design method has developed greatly since it was come up in 1970s. The USA, Canada, Australia, New Zealand and some other developed countries have applied performance-based codes for managing their fire safety problems. First, this kind of design method can overcome limitations when conduct architectural design. At the same time, one of the most important functions of this method is to select the most worthwhile designing scheme which can not only protect fire safety but also expend most reasonably, avoiding the problem of investing inappropriately. Vaughan Beck came up with the concept of cost-benefit evaluation model early in 1979 in his research on fire risk evaluation model called FiRECAM [1]. In addition, British Standard DD240 Fire Safety Engineering in Building [2], Fire Engineering Guidelines of Australia [3] and New Zealand [4] and regulations of some other countries have mentioned the analysis of economy of fire risk for recent years. It proves that the cost-benefit evaluation is an important part of performance-based fire safety design method. However, safety itself is mainly taken into consideration when evaluated, but the economic effectiveness of investment is always ignored in our country. With the advancement of Scientific Outlook on Development, fire safety investments ignoring cost-benefit may not be sustainable. Hence, it is necessary to carry out the evaluation of investment costbenefit when using the method of performance-based fire safety design. And it will form the basis for the decision-making of fire safety investment. 2. The theory of investment cost-benefit in fire safety and the frame of evaluation model 2.1. The theory of investment cost-benefit in fire safety Cost is the price of essential productive factors put into producing activities, which includes the price of labour force, capital and so on. In general, total costs of fire safety in buildings are the prices of productive factors put into building to control or restrain fire risk. Correspondingly, benefit regards to the income brought by cost [5], as to fire safety investment in buildings, its benefit can be divided into two part, one is decrease benefit and the other is value-added benefit. Decrease benefit is the reduced fire losses caused by fire safety investment, and value-added benefit is the increasing part of income from higher production efficiency caused by fire safety investment. Generally speaking, because of the abstract of valueadded benefit, although its contribution to the society cannot be ignored, there isn’t proper way to calculate it. Therefore, benefits discussed in this paper are all about decrease benefits. 2.2. The frame of fire safety investment cost-benefit evaluation model According to the cost and benefit theory from micro economics discussed above, it can be inferred that this cost-benefit model is composed of three parts, one is cost budgets sub-model, one is benefit estimation sub-model, another is analyzing sub-model. For the cost-benefit evaluation in performance-based fire safety design, the cost is due to the improvements of construction fire resistance and the installation of fire safety engineering projects. Meanwhile, the decrease benefits are from these two aspects too. So, figure 1 shows the elementary frame of cost-benefit evaluation model: 3. The cost budgets model of building fire safety design In general, the cost budgets model of building fire safety design can be divided into two parts on the basis of products which are investment in hardware and investment in software. In detail, it can be described by figure 2 and Eq. (1):
537
538
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Fig. 1. Elementary structure of cost-benefit evaluation model
Building Fire Resistance
Hardware Investment
Fire Protection Engineering Projects Evacuation Facilities Extinguishers and Equipment
Cost Budgets
Software Investment
Fire Safety Education and Propagation Fire Safety Management
Fig. 2. The composition of cost budgets
CFP
CFR CST CEG CEP CFS
(1)
3.1. The cost budgets model of building fire resistance For the demand of building fire resistance, four classes of fire resistance have been divided due to Code for fire protection design of buildings [6], and the corresponding fire resistance of structure components of each class have been regulated, either. According to regulations, the cost budgets model of building fire resistance can be composed by doors’ cost, windows’ cost, walls’ cost and others’ cost, which including columns, beams, floors and roofs. By Eq. (2) and data from construction projects cost budgets, the cost budgets of building fire resistance can be calculated.
CDOOR +CWIN +CWALL +COther
CBC
n
¦c
idoor
i 1
m
p
q
j 1
k 1
l 1
+¦ c jwin +¦ ckwall +¦ clother
(2)
3.2. The cost budgets model of fire protection engineering projects Fire protection engineering projects mentioned in this section contain purchase, installation, and maintaining. There are evacuation system, fire alarm system, extinguishing system, smoke control system and fire protection control center in fire protection engineering projects. And the cost of fire protection engineering projects can be calculated by Eq. (3):
CEG
CINSTALL +CMAINTAIN
(3)
According to the theory of construction projects cost budgets, the cost of fire protection installation projects can be divided into 4 parts, as direct fees, indirect fees, profits and taxes. China provinces have different calculation patterns when considering
539
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
budgets according to working drawing from each other. And patterns are recorded in the local regulations including the standard for collecting fees. When budget, local regulations should be complied with [7]. When proper maintaining and fixing work have been done to fire protection systems, it can undoubtedly improve the reliability of them so that to protect more possessions, and enhance the investment benefit. So it is necessary to consider this kind of cost when budgets. Maintaining fees may happen during the whole lifecycle of fire protection systems, thus the time value of funds (a theory in economics) should be considered. The time value of funds means a manifestation of appreciation themselves in a period, which doesn’t take risks and inflation into consideration [5]. The cash flow for the fire protection system during whole lifecycle can be expressed by figure of cash flow like figure 3, in which the horizontal axis represents time period [tˈt+1] (year, month, or so), cash income in time t can be recorded as CI, using symbol “↑”ˈand cash outflow can be recorded as CO, using symbol “↓”, equation CIt-COt=NCFt calls net cash flow in time t.
Fig. 3. Cash flow
There are mainly about 3 kinds of equations may be involved when estimating the costs. They are single payment present worth, equal instalment payment present worth and equal difference payment present worth, which can be calculated respectively by equation (4), (5), (6)˖ F P F (1 i ) n (4) (1 i ) n
P P G
(1 i)n 1 i(1 i)n
(5)
(1 i) n ni 1 i 2 (1 i ) n
(6)
A
The maintaining cost can be estimated by accumulating all of the present worth. 4. Fire loss estimation model One of the most important purposes of performance-based fire safety design method is to protect lives from injuring or dying, therefore, the decrease benefits referred in this paper is mainly about the reduced possession losses in fire due to the increase of fire safety investment. Injuries and deaths are not considered here. For calculating, possession losses in fire needed to be estimated. Recent years, experts all over the world have done some critical researches on fire loss estimation and have gained some achievements. The key of the estimation is to combine fire dynamics with probability theory [8]. When considering fire dynamics, numerous simulation techniques will be applied with software like FDS [9], by the way, the probability theory will work mainly as the form of event trees or so. There are 3 steps to estimate fire loss, the design of fire scenes, gaining the parameters of damage factors by FDS, and the calculation of loss. They’ll be discussed in turn as follows. 4.1. The design of fire scenes Fire scenes can be designed with the method of event tree, which gathers a series of events may happen in a fire in sequence, including the start of fire, the development, the extinguishing movements and the putting out progresses and so on. The fire scenes will differs with different buildings or different fire protection engineering projects. In general, scenes of a fire in a building can be shown as follows by event trees, as figure 4: Total probability Pi of each scene can be worked out by multiplying each probability of sub-scene. 4.2. Gaining the parameters of damage factors Heat radiation, burning, smoking and water are main factors cause damage to building structures, fire protection systems and contents in building. Therefore, temperature, smoke concentration and amount of water using to extinguish are the factors of damage. Once these parameters obtained, the fire direct loss can be estimated with methods discussed as follows.
540
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Fig. 4. Fire scenes event tree in a building
(1) Temperature parameters Including building structures, most of materials in buildings will be influenced by high temperature, which is the principal factor causes damage in a fire. As we know, the resistance of building structures is examined through the experiments of standard fire like ISO834. It means that we’ll classify structures due to the duration they can endure within the standard fire while keep the performance demanded. Once beyond this limit, the structure will be damaged, vice versa. We can conclude that the damage is the result from the mutual effect of time and high temperature. In a similar way, the damages of contents in buildings are also caused by both high temperature and time. If we carry out experiments with typical materials or contents in buildings within a standard fire, according to the changes of materials or contents in the fire, we can judge the damage level of each one. Then, the temperature curve simulated by FDS will be compared to the standard one, using areas enclosed by temperature curves and time axis, as figure 5 shows. Applying equation (7), the probability of damage caused by high temperatures can be estimated. It is noted that once the temperature is too low, no matter how long it lasts, there will not be any damage. So, there should be a lower temperature limit due to different materials or contents.
Figure.5. Standard and FDS fire temperature-time curves
PTD
AFDS ASTANDARD
(7)
(2) Smoke and water parameters Linear interpolation is used to find the individual damages due to smoke and water. Assume that point A(x1, y1) is the lowest threshold of the smoke or water damage where there’ll be no damage and point B (x2, y2) is the highest threshold of the smoke or water damage where there must be damage. They can be joined to form a straight line, where x is threshold value and y is the probability of damage. Figure 6 shows the situation and by the equation (8), the probability of damage caused by smoke or water can be calculated.
541
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Figure.6. Probability of damage versus threshold limits
§ § y2 y 1 · § y2 y 1 · · (8) ¨ ¸ xC ¨¨ y2 ¨ ¸ x2 ¸¸ © x2 x1 ¹ © x2 x1 ¹ ¹ © Concentration of smoke can be obtained from FDS through simulation. For the amount of water, if the heat release rate of the fire is known, a calculation can be done to estimate how much water needed to put out the fire. New Zealand Fire Engineering Design Guide describes a method to calculate it. Due to the method, the amount of water can be worked out and the probability of damage caused by water will be worked out later. (3) Direct fire loss After the simulation through FDS, areas damaged due to the fire should be confirmed. Because of the different damage mechanism among temperature, smoke and water, areas corresponding to each one may differ. Hence, areas should be confirmed respectively according to their parameters of damage factors. Meanwhile, different kinds of contents will suffer differently from the fire, for example, building structures will be damaged by high temperature but be immune to smoke and water nearly. Therefore, density of possessions’ value should be count according to their types or materials. By the way, lots of contents damaged in a fire are not caused by only one factors, but two or three. It cannot simply be added up to make sure the loss whether it may cause counting repeatedly. So, according to damage mechanism, areas damaged by the fire can be divided into 3 parts in general as figure 7 shows: yC
Figure.7. Areas damaged by different factor
It is assumed that the ignition point is the center of a circle and the fire will spread to surroundings as circle. Damages caused by flame is regarded as the most serious situation because almost everything in this circle loses their value and can’t be repaired. Areas damaged by water is larger than that caused by flame due to the high temperature may start sprinklers or so and due to actions by fire brigade. The largest area damaged in fire is the one by smoke and the direct losses in this areas may be the most modest one because numerous of things can be restored or can still maintain some value. However, different places will have different ways to divide the damaged areas. As when a fire happened in an electronic instruments plant, damaged areas can be divided into 4 parts, because damages caused by mixtures of smoke and water will be fatal to these electronic equipments. After simplification, it can be expressed by equation (9) that can estimate the direct loss in a fire:
DL ZT AT PTD ZS AS PSD ZW AW PWD
(9)
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You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Generally, indirect loss caused by a fire are much more than direct loss. We can assume the indirect loss is n times more than direct loss [10], so the total loss in a fire can be estimated by equation (10): L DL IL DL nDL DL(1 n) (10)
5. Cost-benefit analysis of fire safety investment to a building Method of net present worth is applied in this paper to carry out the analysis. The principle is to transform all cash flow during the whole lifecycle into present cash flow, using a discount rate i. If the net present worth is more than 0, the investment can be accepted. For fire safety investment to a building, costs include installation and maintaining of fire protection engineering, and benefits are mainly about the reduced losses brought about by costs. So, equation of cost-benefit analysis can be expressed as equation (11): NPV (i ) B C L (CBC CEG ) (11) It is the simplest and most basic method to estimate whether the performance-based fire safety design scheme is appropriate. Anyway, there being multiple of methods which can estimate the cost-benefit analysis more delicately and more definitely will not be discussed in this paper confined to the length. 6. Conclusion It will be more scientific and suitable when making decisions about fire safety investment by evaluating cost-benefit on account of performance-based fire safety design. The evaluation model consists of cost budgets model, fire loss estimation model and cost-benefit analysis model. They were built in this paper and the cost budgets model can be divided into cost of fire resistance and cost of fire protection engineering projects; while fire loss estimation model is mainly about the discussion of damage caused by temperature, smoke and water and the respective loss. The basic frame of the evaluation model was built integrally in the paper, but there still be a large amount of details that should be studied later. Especially the statistics of building fire and damage situation should be collected on purpose and more specifically. And the fire insurance should be considered in next researches due to its significant influences on cost-benefit analysis. It should be noted that the result calculated within the model can just be compared with each other but not the realistic one. However, with the development of fire dynamics, statistics and simulation techniques, it will be more and more similar to the real fire one day.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
Beck, V.R. A Cost-Effective Decision-Making Model for Building Fire Safety and Protection. Fir Safety Journal, 1987, 12: 121-138. British Standard DD240. Fire Safety Engineering in Building. Part 1: Guide to the Application of Fire Safety Engineering Principles. London, 1997. Australian Government and States and Territories of Australia. Guide to the BCA 2008. Canberra: 2008. New Zealand Government. The Building Regulations 1992. Wellington: 1992. LI Yi-yuan. Western Economics (Micro). Beijing: Tsinghua University Press, 1998. Ministry of Public Security. Code for fire protection design of buildings. Beijing: 2014. HAN Xue-feng, WANG Li. Preliminary Budget of Fire Protection System. Beijing: Mechanical Industry Press, 2013. ZHU Guan-quan. Fire Risks Researches Based on Fire dynamics and Statistics. Hefei: University of Science and Technology of China, 2007. TIAN Yu-min, YANG Yan-jun. Study on Quantification Methods of Fire Losses in a Building Based On Numerical Simulation. Proceedings of 2010(Shenyang) International Colloquium on Safety Science and Technology. [10] TIAN Yu-min. Fire Safety Economics. Beijing: Chemical Industry Press, 2007.
ScienceDirect Procedia Engineering 135 (2016) 536 – 542
Research on cost-benefit evaluation model for performance-based fire safety design of buildings You-wei Zhang* Chinese People’s Armed Police Force Academy, 220 Xichang Road, Langfang 065000, China
Abstract One of the most important functions of performance-based fire safety design method is to evaluate the economic efficiency of different schemes so that to make the fire safety investment more reasonable. It should begin with the calculation of cost budgets and benefits when evaluate the investment efficiency. Costs for improving building fire resistance and installing fire engineering projects are included in the investment budgets. However, the investment benefits are mainly about the reduced losses after the enhancement of the building fire safety level. Based on the performance-based fire safety design method, applying principles of economics and construction budget, the model described above will be built in this paper to provide scientific guides for fire safety investment. © Authors. Published by Elsevier Ltd. This an open accessunder articleCC under the CC BY-NC-ND ©2016 2016The The Authors. Published by Elsevier Ltd.isOpen access BY-NC-ND license. license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of School of Engineering of Sun Yat-sen University. Peer-review under responsibility of the organizing committee of ICPFFPE 2015
.
Keywords: performance-based fire safety design; cost-benefit analysis; cost budget; loss estimation
Nomenclature
cost of doors
cidoor c jwin
cost of window j
CWIN
cost of windows
ckwall
cost of wall k
CWALL
cost of walls
clother
cost of other component l
COther n
cost of columns, beams, floors and roofs
CEG
cost of fire protection engineering projects
amount of doors
CINSTALL
cost of fire protection installation projects
m
amount of windows
cost of fire protection maintaining projects
p q yC DL IL
amount of walls amount of others probability of damage direct loss of building in a fire indirect loss of building in a fire
CMAINTAIN F A xC L AT
AS
areas damaged by smoke (m2)
AW
areas damaged by water (m2)
PTD
probability of temperature damage
PSD
probability of smoke damage
CBC
cost of building structure
CDOOR
cost of door i
an investment in a year future an investment in each year future maximum value of factor causing damage total losses of building in a fire areas damaged by temperature (m2)
* Corresponding author. Tel.: +86-13503260747. E-mail address: [email protected]
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICPFFPE 2015
doi:10.1016/j.proeng.2016.01.096
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Aoverlap
PWD
probability of temperature damage
G
an increasing amount of investment in each year future (Yuan)
areas damaged by three factors(m2)
Poverlap probability of damage caused by three factors
ZW
density of possessions’ value caused by water (Yuan/m2)
ZT
density of possessions’ value caused by temperature (Yuan/m2)
ZS
density of possessions’ value caused by smoke (Yuan/m2)
P
present worth of each investment in the future areas enclosed by FDS temperature curve and time axis
AFDS
ASTANDARD areas enclosed by standard fire temperature curve and time axis 1. Introduction Performance-based fire safety design method has developed greatly since it was come up in 1970s. The USA, Canada, Australia, New Zealand and some other developed countries have applied performance-based codes for managing their fire safety problems. First, this kind of design method can overcome limitations when conduct architectural design. At the same time, one of the most important functions of this method is to select the most worthwhile designing scheme which can not only protect fire safety but also expend most reasonably, avoiding the problem of investing inappropriately. Vaughan Beck came up with the concept of cost-benefit evaluation model early in 1979 in his research on fire risk evaluation model called FiRECAM [1]. In addition, British Standard DD240 Fire Safety Engineering in Building [2], Fire Engineering Guidelines of Australia [3] and New Zealand [4] and regulations of some other countries have mentioned the analysis of economy of fire risk for recent years. It proves that the cost-benefit evaluation is an important part of performance-based fire safety design method. However, safety itself is mainly taken into consideration when evaluated, but the economic effectiveness of investment is always ignored in our country. With the advancement of Scientific Outlook on Development, fire safety investments ignoring cost-benefit may not be sustainable. Hence, it is necessary to carry out the evaluation of investment costbenefit when using the method of performance-based fire safety design. And it will form the basis for the decision-making of fire safety investment. 2. The theory of investment cost-benefit in fire safety and the frame of evaluation model 2.1. The theory of investment cost-benefit in fire safety Cost is the price of essential productive factors put into producing activities, which includes the price of labour force, capital and so on. In general, total costs of fire safety in buildings are the prices of productive factors put into building to control or restrain fire risk. Correspondingly, benefit regards to the income brought by cost [5], as to fire safety investment in buildings, its benefit can be divided into two part, one is decrease benefit and the other is value-added benefit. Decrease benefit is the reduced fire losses caused by fire safety investment, and value-added benefit is the increasing part of income from higher production efficiency caused by fire safety investment. Generally speaking, because of the abstract of valueadded benefit, although its contribution to the society cannot be ignored, there isn’t proper way to calculate it. Therefore, benefits discussed in this paper are all about decrease benefits. 2.2. The frame of fire safety investment cost-benefit evaluation model According to the cost and benefit theory from micro economics discussed above, it can be inferred that this cost-benefit model is composed of three parts, one is cost budgets sub-model, one is benefit estimation sub-model, another is analyzing sub-model. For the cost-benefit evaluation in performance-based fire safety design, the cost is due to the improvements of construction fire resistance and the installation of fire safety engineering projects. Meanwhile, the decrease benefits are from these two aspects too. So, figure 1 shows the elementary frame of cost-benefit evaluation model: 3. The cost budgets model of building fire safety design In general, the cost budgets model of building fire safety design can be divided into two parts on the basis of products which are investment in hardware and investment in software. In detail, it can be described by figure 2 and Eq. (1):
537
538
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Fig. 1. Elementary structure of cost-benefit evaluation model
Building Fire Resistance
Hardware Investment
Fire Protection Engineering Projects Evacuation Facilities Extinguishers and Equipment
Cost Budgets
Software Investment
Fire Safety Education and Propagation Fire Safety Management
Fig. 2. The composition of cost budgets
CFP
CFR CST CEG CEP CFS
(1)
3.1. The cost budgets model of building fire resistance For the demand of building fire resistance, four classes of fire resistance have been divided due to Code for fire protection design of buildings [6], and the corresponding fire resistance of structure components of each class have been regulated, either. According to regulations, the cost budgets model of building fire resistance can be composed by doors’ cost, windows’ cost, walls’ cost and others’ cost, which including columns, beams, floors and roofs. By Eq. (2) and data from construction projects cost budgets, the cost budgets of building fire resistance can be calculated.
CDOOR +CWIN +CWALL +COther
CBC
n
¦c
idoor
i 1
m
p
q
j 1
k 1
l 1
+¦ c jwin +¦ ckwall +¦ clother
(2)
3.2. The cost budgets model of fire protection engineering projects Fire protection engineering projects mentioned in this section contain purchase, installation, and maintaining. There are evacuation system, fire alarm system, extinguishing system, smoke control system and fire protection control center in fire protection engineering projects. And the cost of fire protection engineering projects can be calculated by Eq. (3):
CEG
CINSTALL +CMAINTAIN
(3)
According to the theory of construction projects cost budgets, the cost of fire protection installation projects can be divided into 4 parts, as direct fees, indirect fees, profits and taxes. China provinces have different calculation patterns when considering
539
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
budgets according to working drawing from each other. And patterns are recorded in the local regulations including the standard for collecting fees. When budget, local regulations should be complied with [7]. When proper maintaining and fixing work have been done to fire protection systems, it can undoubtedly improve the reliability of them so that to protect more possessions, and enhance the investment benefit. So it is necessary to consider this kind of cost when budgets. Maintaining fees may happen during the whole lifecycle of fire protection systems, thus the time value of funds (a theory in economics) should be considered. The time value of funds means a manifestation of appreciation themselves in a period, which doesn’t take risks and inflation into consideration [5]. The cash flow for the fire protection system during whole lifecycle can be expressed by figure of cash flow like figure 3, in which the horizontal axis represents time period [tˈt+1] (year, month, or so), cash income in time t can be recorded as CI, using symbol “↑”ˈand cash outflow can be recorded as CO, using symbol “↓”, equation CIt-COt=NCFt calls net cash flow in time t.
Fig. 3. Cash flow
There are mainly about 3 kinds of equations may be involved when estimating the costs. They are single payment present worth, equal instalment payment present worth and equal difference payment present worth, which can be calculated respectively by equation (4), (5), (6)˖ F P F (1 i ) n (4) (1 i ) n
P P G
(1 i)n 1 i(1 i)n
(5)
(1 i) n ni 1 i 2 (1 i ) n
(6)
A
The maintaining cost can be estimated by accumulating all of the present worth. 4. Fire loss estimation model One of the most important purposes of performance-based fire safety design method is to protect lives from injuring or dying, therefore, the decrease benefits referred in this paper is mainly about the reduced possession losses in fire due to the increase of fire safety investment. Injuries and deaths are not considered here. For calculating, possession losses in fire needed to be estimated. Recent years, experts all over the world have done some critical researches on fire loss estimation and have gained some achievements. The key of the estimation is to combine fire dynamics with probability theory [8]. When considering fire dynamics, numerous simulation techniques will be applied with software like FDS [9], by the way, the probability theory will work mainly as the form of event trees or so. There are 3 steps to estimate fire loss, the design of fire scenes, gaining the parameters of damage factors by FDS, and the calculation of loss. They’ll be discussed in turn as follows. 4.1. The design of fire scenes Fire scenes can be designed with the method of event tree, which gathers a series of events may happen in a fire in sequence, including the start of fire, the development, the extinguishing movements and the putting out progresses and so on. The fire scenes will differs with different buildings or different fire protection engineering projects. In general, scenes of a fire in a building can be shown as follows by event trees, as figure 4: Total probability Pi of each scene can be worked out by multiplying each probability of sub-scene. 4.2. Gaining the parameters of damage factors Heat radiation, burning, smoking and water are main factors cause damage to building structures, fire protection systems and contents in building. Therefore, temperature, smoke concentration and amount of water using to extinguish are the factors of damage. Once these parameters obtained, the fire direct loss can be estimated with methods discussed as follows.
540
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Fig. 4. Fire scenes event tree in a building
(1) Temperature parameters Including building structures, most of materials in buildings will be influenced by high temperature, which is the principal factor causes damage in a fire. As we know, the resistance of building structures is examined through the experiments of standard fire like ISO834. It means that we’ll classify structures due to the duration they can endure within the standard fire while keep the performance demanded. Once beyond this limit, the structure will be damaged, vice versa. We can conclude that the damage is the result from the mutual effect of time and high temperature. In a similar way, the damages of contents in buildings are also caused by both high temperature and time. If we carry out experiments with typical materials or contents in buildings within a standard fire, according to the changes of materials or contents in the fire, we can judge the damage level of each one. Then, the temperature curve simulated by FDS will be compared to the standard one, using areas enclosed by temperature curves and time axis, as figure 5 shows. Applying equation (7), the probability of damage caused by high temperatures can be estimated. It is noted that once the temperature is too low, no matter how long it lasts, there will not be any damage. So, there should be a lower temperature limit due to different materials or contents.
Figure.5. Standard and FDS fire temperature-time curves
PTD
AFDS ASTANDARD
(7)
(2) Smoke and water parameters Linear interpolation is used to find the individual damages due to smoke and water. Assume that point A(x1, y1) is the lowest threshold of the smoke or water damage where there’ll be no damage and point B (x2, y2) is the highest threshold of the smoke or water damage where there must be damage. They can be joined to form a straight line, where x is threshold value and y is the probability of damage. Figure 6 shows the situation and by the equation (8), the probability of damage caused by smoke or water can be calculated.
541
You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Figure.6. Probability of damage versus threshold limits
§ § y2 y 1 · § y2 y 1 · · (8) ¨ ¸ xC ¨¨ y2 ¨ ¸ x2 ¸¸ © x2 x1 ¹ © x2 x1 ¹ ¹ © Concentration of smoke can be obtained from FDS through simulation. For the amount of water, if the heat release rate of the fire is known, a calculation can be done to estimate how much water needed to put out the fire. New Zealand Fire Engineering Design Guide describes a method to calculate it. Due to the method, the amount of water can be worked out and the probability of damage caused by water will be worked out later. (3) Direct fire loss After the simulation through FDS, areas damaged due to the fire should be confirmed. Because of the different damage mechanism among temperature, smoke and water, areas corresponding to each one may differ. Hence, areas should be confirmed respectively according to their parameters of damage factors. Meanwhile, different kinds of contents will suffer differently from the fire, for example, building structures will be damaged by high temperature but be immune to smoke and water nearly. Therefore, density of possessions’ value should be count according to their types or materials. By the way, lots of contents damaged in a fire are not caused by only one factors, but two or three. It cannot simply be added up to make sure the loss whether it may cause counting repeatedly. So, according to damage mechanism, areas damaged by the fire can be divided into 3 parts in general as figure 7 shows: yC
Figure.7. Areas damaged by different factor
It is assumed that the ignition point is the center of a circle and the fire will spread to surroundings as circle. Damages caused by flame is regarded as the most serious situation because almost everything in this circle loses their value and can’t be repaired. Areas damaged by water is larger than that caused by flame due to the high temperature may start sprinklers or so and due to actions by fire brigade. The largest area damaged in fire is the one by smoke and the direct losses in this areas may be the most modest one because numerous of things can be restored or can still maintain some value. However, different places will have different ways to divide the damaged areas. As when a fire happened in an electronic instruments plant, damaged areas can be divided into 4 parts, because damages caused by mixtures of smoke and water will be fatal to these electronic equipments. After simplification, it can be expressed by equation (9) that can estimate the direct loss in a fire:
DL ZT AT PTD ZS AS PSD ZW AW PWD
(9)
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You-wei Zhang / Procedia Engineering 135 (2016) 536 – 542
Generally, indirect loss caused by a fire are much more than direct loss. We can assume the indirect loss is n times more than direct loss [10], so the total loss in a fire can be estimated by equation (10): L DL IL DL nDL DL(1 n) (10)
5. Cost-benefit analysis of fire safety investment to a building Method of net present worth is applied in this paper to carry out the analysis. The principle is to transform all cash flow during the whole lifecycle into present cash flow, using a discount rate i. If the net present worth is more than 0, the investment can be accepted. For fire safety investment to a building, costs include installation and maintaining of fire protection engineering, and benefits are mainly about the reduced losses brought about by costs. So, equation of cost-benefit analysis can be expressed as equation (11): NPV (i ) B C L (CBC CEG ) (11) It is the simplest and most basic method to estimate whether the performance-based fire safety design scheme is appropriate. Anyway, there being multiple of methods which can estimate the cost-benefit analysis more delicately and more definitely will not be discussed in this paper confined to the length. 6. Conclusion It will be more scientific and suitable when making decisions about fire safety investment by evaluating cost-benefit on account of performance-based fire safety design. The evaluation model consists of cost budgets model, fire loss estimation model and cost-benefit analysis model. They were built in this paper and the cost budgets model can be divided into cost of fire resistance and cost of fire protection engineering projects; while fire loss estimation model is mainly about the discussion of damage caused by temperature, smoke and water and the respective loss. The basic frame of the evaluation model was built integrally in the paper, but there still be a large amount of details that should be studied later. Especially the statistics of building fire and damage situation should be collected on purpose and more specifically. And the fire insurance should be considered in next researches due to its significant influences on cost-benefit analysis. It should be noted that the result calculated within the model can just be compared with each other but not the realistic one. However, with the development of fire dynamics, statistics and simulation techniques, it will be more and more similar to the real fire one day.
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